hello and welcome to HCM forum,
I am glad you posted your query,
i would like to inform you that following band application some sort of trauma to gums occurs which causes them to be sore .
gums around the tooth become sore, swollen and sometimes bleeding occurs.
but there is nothing to be concerned about , normally healing takes about 10 to 15 days.
i would recommend you to see your dentist
as he/she might prescribe an ointment which will promote healing and provide pain relief.
perform warm saline rinses(3-4 times/day) to relief pain and swelling.
i hope i answered your query.
i wish you good health,